It's good to have lots of links. It's particularly good to have links from sites with a good page rank. However, I think that individual pages are ranked. So a site could have a high page rank on its homepage but a low one on its links page. Is that right? And if so does Google go by the homepage rank or the actual page that the link comes from? Or am I barking up the wrong tree?

It's the page the link is on. As I understand it, the page's rank is also pro-rata'ed between links, so if your link is on a page with lots of outbound links, you'll get less of that page's rank than if you were the only link.

Yes, it goes by the PR of the page the link is on. Also, the closer to the top of the page the better the link. Try getting links with your specific keywords in mind. For example: If you have a site that sells roller skates, you should ask for your links to be named "roller skates". Also, try to find lesser known keywords. For example: Roller Skates Indiana would have far less competition for rankings than "roller skates". Use the smaller competition keywords to target your customers.